This isn't a -tabstat- issue as such. -tabstat-
just passes the buck to -summarize-, which
behaves in the same way.
The issue is delicate, but hinges, I surmise,
on this distinction. When -summarize- (e.g.) _uses_
the sum of the weights, it rescales first.
As quoted, [U] 14.1.6 includes the expression
"when it uses them", which thus appears not
ornamental, but crucial.
When -summarize- _displays_ the sum of the
weights, it displays the unscaled sum.

Good point, although it still leaves open the question of why it behaves
this way. A long-standing oversight or bug? Sound statistical practice?
(If so, it wouldn't be the first time Stata has surprised me by not doing
what I expected, and then having it turn out that Stata was right.) Should
-tabstat- be modified so it doesn't just pass the buck to -summarize-?